I looked at two previous threads that solved this by unlocking the offending fonts, or putting the fonts into the Applications > IndesignCS6 > Fonts folder. Neither of these solutions worked for me. Any advice is greatly appreciated.

I have not. I'm not even entirely sure what that means. Though, I do have the files set to "read & write" for everyone. I'm on a brand new MacBook Pro, and CS6 was the first and only installation of ID CS6 and the fonts used.

Did you try downloading a free utility like FontFinagler or FontNuke and running the utilty so that it deletes and resets the font plist cache (assuming Mac OS)? After a refresh of fonts plist and a reboot for good measure, see if that helps the situation.

I just sucessfully packaged the file with the problem fonts in InDesign CS5. I think the issue had something to do with the problem font being a Postscript Type 1 format. Does CS6 no longer support packaging this type of font format?

InDesign still works with PostScript Type 1, but you should make a conscious effort to replace any T1 with OTF format. Less crashing, less issues, more robust when you clean out the aging PS T1 fonts. Try FontFinagler or FontNuke. It cannot hurt you.